Journal of Integer Sequences, Vol. 26 (2023), Article 23.6.3

The Sixth Moment of Random Determinants

Dominik Beck
Faculty of Mathematics and Physics
Charles University
Prague 11636
Czech Republic

Zelin Lv and Aaron Potechin
The University of Chicago
Chicago, IL 60637


We determine the sixth moment of the determinant of an asymmetric n × n random matrix where the entries are drawn independently from an arbitrary distribution Ω over R with mean 0. Furthermore, we derive the asymptotic behavior of the sixth moment of the determinant as the size of the matrix tends to infinity.

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(Concerned with sequences A000142 A052127 A357571.)

Received October 3 2022; revised versions received February 24 2023; June 13 2023; June 15 2023. Published in Journal of Integer Sequences, June 17 2023.

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